Apparatus for developing a trigonometric function of an angle



Sept. 16, 1958 Filed Sept. 15, 1955 J. K. STORY 2,852,190

APPARATUS FOR DEVELOPING A TRIGONOMETRIC FUNCTION OF AN ANGLE 2 Sheets-Sheet 1 ak /mask Sraey,

INVENTOR.

Sept. 16, 1958 J. K. STORY 2, 2

APPARATUS FOR DEVELOPING A TRIGONOME'IRIC FUNCTION OF AN ANGLE Filed Sept. 15, 1955 2 Sheets-Sheet 2 314 4455 k Sway,

IN V EN TOR.

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United States Patent APPARATUS FOR DEVELOPING A TRrGoNo- METRIC FUNCTION OF AN ANGLE James Story, Long Beach, Calif., assignor to V. E. Kuster, Long Beach, Calif.

Application September 15, 1955, Serial No. 534,593

12 Claims. (Cl. 23561) This invention relates to improved devices to be used in computing apparatus and the like, for developing signals corresponding to the sine or cosine of an angle. This application is a continuation-in-part of my copending application Serial No. 465,281, filed October 28, 1954, now Patent No. 2,843,941, on Well Surveying Apparatus, and covers subject matter which was required to be divided from that application.

In computing apparatus, it sometimes becomes desirable to employ a resolving unit which is actuated in accordance with variations in a particular angle and which responds to such actuation by developing an output signal corresponding to the sine or cosine of that angle. The general object of the present invention is to provide a resolver of this type which is so designed as to be inherently more reliable and accurate than prior similar devices. At the same time, a resolver embodying the invention is structurally very simple and positive acting.

In accordance with the invention, the resolver includes a pair of rotary elements which are mounted for rotation in correspondence one with the other, but reversely, about a pair of spaced essentially parallel axes. These rotary elements are turned to positions corresponding to the input angle, and serve to actuate an output unit, preferably an electrical resistance or potentiometer which is connected to the two elements at eccentric locations. The mounting of the output unit is such that, as the two rotary elements turn, a line extending between the two points at which the rotary elements are connected to the output unit remains parallel to a line joining the two axes of the rotary elements. As the rotary elements turn in reverse directions, the two eccentric points of connection move toward and away from each other, to actuate the output unit connected thereto and thereby develop the desired trigonometric function. In certain instances, two such potentiometers or other output units may be employed, to develop both the sine and cosine of the angle.

To effectively coordinate the reverse rotation of the two rotary elements, these elements may be a pair of wheels having gear teeth which operatively connect the two wheels together. Preferably, the teeth of one wheel directly mesh with and drive the teeth of the other wheel.

The above and other features and objects of the present invention will be better understood from the following detailed description of the typical embodiment illustrated in the accompanying drawing in which:

Fig. 1 is a side elevational view 'of a sine-cosine generating device constructed in accordance with the invention;

Fig. 2 is a plan view taken on line 22 of Fig. 1;

Fig. 3 is an enlarged fragmentary section taken on line 3-3 of Fig. 1;

Fig. 4 is an enlarged section through one of the potentiometers of the device; and

Fig. 5 is a circuit diagram'of a multiplying circuit into which the Fig. 1 device may be connected.

In the drawing, I have shown at a device which is ice Fatented Sept. 16, 1958 adapted to be actuated by a motor 11 to positions representing different angles, and including a pair of potentiometer units 12 and 13 which act to automatically adjust to positions representing the sine and cosine respectively of the angle. Unit 10 includes a pair of preferably identical gears 14 and15, which are individually mounted for rotation about spaced parallel axes 16 and 317, and whose teeth 18 mesh at 19 to interconnect the gears for rotation in correspondence but reversal. These gears 14 and are turned by the motor to different angular positions, and act to carry and actuate the two potentiometer's 12 and 13. j

The various working parts of unit 10 may be m'ovably mounted to a stationary rigid supporting plate 20, with gears 14 and 15 lying in a plane which is parallel to but spaced at short distance outwardly from the plane of plate 20p Opposite gears 14 and 15, plate 20 contains a pair of circular openings 21, which merge together opposite the location 19 to form together an aperture essentially of figure 8 configuration. The two gears are mounted for rotation about their axes 16 and 17 by means of six rollers 22, 23, 24, 25, 26 and 27, which are mounted by shafts 28 and bearings 29 for rotation about axes extending parallel to axes 16 and 17. As best seen in Fig. 3, each of the rollers 22 contains an annular peripheral groove 30 which receives the outer toothed portion of one of the gears 14 or 15, and whose outer cylindrical bearing surfaces 31 engage annular shoulders or bearing surfaces 32 at opposite axial sides of the gear.

The three rollers 22, 23 and 24 rotatably engage gear 14 at three evenly circularly spaced locations, as shown, while the three rollers 25, 26 and 27 correspondingly engage and rotatably mount gear 15. Preferably, the shafts 28 which mount rollers 22, 25, 26 and 27 are attached to mounting plate 20 by eccentric portions 33, which allow limited adjustment of the carried rollers toward and away from gears 14 and 15, so that the gears may be held accurately against shifting movement relative to their desired axes, and in a manner preventing backlash between the two gears. When the rollers 22 are properly adjusted, nuts 34 may be tightened on the eccentric portions 33 of shafts 28, to retain the shafts in the desired adjusted positions. The two rollers 23 and 24 may be rigidly mounted to plate 20 by shafts similar to the shaft 28 shown in Fig. 3, but whose portions 33 are alined axially with the roller carrying portions of these shafts, rather than being eccentric.

The electric motor 11 may be mounted to plate 20, and acts to drive gears 14 and 15 to different rotary positions by means of a gear system typically represented at 35. The angular positioning of gears 14 and 15 may be indicated by suitable markings 36 on the gear 14, coacting with an index marking or pointer 37 rigidly attached to plate 20. A zero position of gear 14 may be indicated by registry of a zero marking 38 on the .gear with index marking 37; When gear 14 is turned to a different angular position, the angle a between zero marking 38 and index marking 37 is indicated by the particular angle marking 36 on wheel 14 which is opposite pointer 37 in the changed position.

The two potentiometers 12 and 13 are of the linear motion and linear winding type, and are preferably substantially identical. As best seen in Fig. 4, each of these potentiometers may include a tubular elongated outer housing or body 39 containing and rigidly carrying an elongated resistor element 40 extending axially of the body. Element 40 may comprise a large number of turns of wire wound about an elongated electrically insulative carrier member 41. An actuating rod 42 is mounted for only axial sliding movement relative to and within the housing or body 39, and carries a sliding con tact 43 which electrically engages and moves along resistor element 40. Rod 42 may be mounted for its sliding movement by means of a guide member 44 which extends about and is slideable along a guide rod attached to body 39. Also, a restricted opening 46 formed at the end of body 39 may assist in guiding rod 42 for the desired sliding movement. As will be apparent, contact 43 is of course suitably insulated from resistor element 40, as by forming rod 42 and element 44 of electrically insulative material.

The body 39 of potentiometer 12 is pivotally connected to a pin 47 which projects laterally from gear 14 at an eccentric location with respect to axis 16, while rod 42 is pivotally connected at an opposite end of the potentiometer unit to a similar pin 48 projecting laterally from gear 15.. Pins 47 and 48 desirably extend parallel to axes 16 and 17, and are connected to elements 39 and 42 for relative pivotal movement about the longitudinal axes 49 and of pins 47 and 48.

Pins 47 and 48 are located identical distances from axes 16 and 17 respectively, and are so positioned as to maintain all positions of potentiometer 12 mutually parallel. For this purpose, pin 47 crosses the line 150 between axes 16 and 17 at the same instant that pin 48 crosses that line. Similarly, pins 47 and 48 reach the uppermost point of their travel at the same instant or position of the gears, and the same is true of their lowermost positions. Stated differently, the mounting of the parts is such that, as gears 14 and 15 turn, a line joining together the two axes 49 and 50 of pins 47 and 48 always remains parallel to the line 150 which interconnects axes 16 and 17.

The winding 40 of each of the potentiometers 12 and 13 is of the linear type, so that the rate of change of resistance of winding 40 is uniform along the entire range of movement of contact 43. The winding 40 of each potentiometer may be connected into an electrical circuit by means of a pair of leads connected to its opposite ends, and by means of a center tap 53. In the case of potentiometer 12, center tap 53 is so located as to be engaged by contact 43 exactly when pins 47 and 48 are located either directly above or directly beneath axes 16 and 17 respectively. That is, the center tap is reached when potentiometer 12 is in either its uppermost position or its lowermost position.

The second potentiometer 13 is mounted to gears 14 and 15 at a side opposite that at which potentiometer 12 is mounted. The potentiometer 13 is attached to the gears by a pair of pins 47a and 48a which correspond to pins 47 and 48, but which are oifset 90 about the gear axes from pins 47 and 48 respectively. As in the case of potentiometer 12, the center tap 53a of potentiometer 13 (connected to the center of winding 40a) engages movable contact 43a of that potentiometer when potentiometer 13 is in either its uppermost or lowermost position, with pins 47a and 48a in direct vertical alincment with axes 16 and 17 When the center tapped potentiometers are mounted in the defined manner, and gears 14 and 15 are driven by motor 11 to rotary positions corresponding to a particular angle a, the settings of potentiometers 12 and 13 are accurately proportional to the cosine and sine respectively of angle a. That is, the resistance between the movable contact 43 and center tap 53 of potentiometer 12 corresponds to the cosine of angle a, while the resistance between movable contact 4311 and center tap 53a of potentiometer 13 corresponds to the sine of that angle. The provision of center taps on the two potentiometers allows the potentiometers to be used for generating the sine and cosine of angle a through the entire 360 rotation of gears 14 and 15.

Fig. 5 shows a typical multiplier circuit into which the potentiometers 12 and 13 of theresolving or generating device 10 may be connected, to multiply the generated sine or cosine of angle a by a desired value or number. This circuit is energized by a suitable D. C. power Source 4 having a positive side 54, a negative side 154, and a point 254 of intermediate or zero potential half way between the potentials of points 54 and 154. As a typical example, the power source is shown as including two identical batteries 354, one connected between points 154 and 254, and the other between points 254 and 54. Center tap 53 of potentiometer 12 (or 13) is connected to the intermediate potential lead 254. The two opposite ends of potentiometer winding 40 are connected respectively to the movable contacts of a pair of potentiometers 55 and 56, which are interlocked by a mechanical control represented at 57 for actuation in unison to positions representing a value or setting to be multiplied by the sine or cosine represented by the setting of poteutiometer 12. The resistor element of potentiometer 55 is connected to power leads 54 and 254, in series with a resistor 58. Similarly, the resistor element of potentiometer 56 is connected to leads 154 and 254, in series with a resistor 59. Thus, the circuit of Fig. 5 forms in efiect two conventional multiplier circuits, one of which includes resistor 58, potentiometer S5, and the upper half of winding 40 of potentiometer 12, and the second of which includes resistor 59, potentiometer 56, and the lower half of potentiometer 12. The first of these multiplier circuits is effective when the movable contact of potentiometer 12 is above the center tap 53, while the second of the circuits is effective when the movable contact is below the center tap. Together, these two multiplier circuits act to maintain between the movable contact of potentiometer 12 and center tap 53 a potential which is proportional to the cosine of angle a times a value or number represented by the potentiometers 55 and 56. To obtain mechanical movement corresponding to the product represented by the potential between contact 43 and center tap 53, I employ a readout potentiometer 60, whose center tap is connected by lead to the center tap of potentiometer 12, and whose resistor ends 260 and 369 are connected to the power leads 54 and 154 respectively through a pair of resistors 61 and 62. The movable contacts of potentiometers 12 and 60 are connected to the input side of an amplifier 63, which supplies to a motor 64 an amplified potential corresponding to the difference in potential between the two different contacts. Motor 64 acts as a null balance motor, which serves when energized by a difference in potential between the movable contacts of potentiometers 12 and 60, to mechanically move the movable contact of the latter potentiometer (through a drive represented at 65) to a position in which there is no difference in potential between the movable contacts of the potentiometers. Thus, the movable contact of potentiometer 60 is moved in proportion to the variations in potential between the movable contact of potentiometer 12 and center tap 53. The shaft of motor 64 also turns to positions which are proportional to the defined potential, so that the positioning of the shaft of motor 64 represents the desired multiplication product. Consequently, that shaft may be connected to any suitable type of indicator 66, to indicate directly the product. As will be apparent, the sine generating potentiometer 13 may also be connected into a circuit similar to that shown in Fig. 5, to multiply the sine of angle a by a desired value.

The potentiometers 12 and 13 generate very accurately the cosine and sine respectively of any angle a within the entire 360 range of rotary movement of gear 14. However, it is desirable also in certain instances to know in which .of the four quadrants the angle a lies. This is desirable, for instance, where the apparatus may be utilized in a well surveying instrument such as that shown in my copending application Serial No. 452,649. In that case, the angle a represents the direction of inclination of a bore hole relative to the true vertical, and the direction of inclination is true North when zero marking 38 registers with pointer 37. For indicating the quadrant in which angle a lies, I provide an additional indicating unit represented generally at 67 in Fig. 1.

For indicating whether pointer 37 is opposite the North half of gear 14 or its South half (considering zero marking 38 as true North), I provide an indicator element 68 having formed on it the letters N (-for North), and S (for South). This element may be positioned behind a window 69 in the wall of an indicator board 70, and may be mounted for pivotal movement about an axis 71 between the tull line and broken line positions of Fig. 1. The letter N is formed on element 68 at 72, and is visible through window 69 in the full line position of element 68, while the letter S is formed at 73, and is visible in the broken line position of element 68. Element 68 has an arcuate portion 74 formed of metallic metal, which is movable into and serves as the armature of a solenoid 75. When solenoid 75 is energized, it draws element 68 to the full line position of Fig. 1, while element 68 returns to the broken line position under the influence of a spring 76 when coil 75 is de-energized.

The energization of coil 75 by battery 77 is controlled by a switch unit 78. This switch unit comprises a rotatable shaft 79, which is driven by motor 11 through a drive connection represented at 111, and in a one to one ratio with gear 14, and which carries two electrical contacts 80 and 81 rotatable with shaft 79. These contacts turn to positions representing exactly the angle a. Contact 80 is engageable with a semicircular contact 82 as long as contact 80 is in the upper or northern half of its course of circular travel about the axis of shaft 79, that is, as long as the angle a is in a northerly rather than southerly direction. If the angle a is in a southerly direction (i. e., if pointer 37 is opposite the half of gear 14 which represents a southern direction), the contact between movable contact 80 and stationary contact 82 is broken. As seen in Fig. 1, the switch formed by contacts 80 and 82 is connected into the energizing circuit of coil 75, to thus cause element 68 to indicate through window 69 whether the angle a is in a northerly or southerly direction.

Adjacent the element 68, for giving an east-west indication, there is provided an element 83, corresponding to element 68 but carrying a letter W at 84 and the letter E at 85. This element 83 is actuated by a solenoid 86, under the control of rotatable contact 81, which engages a semicircular stationary contact 87 when the angle a is in an easterly direction, to thus close the energizing circuit to coil 86, but breaks this circuit when the angle is in a westerly direction.

I claim:

1. A trigonometric resolver comprising two members mounted for rotation about spaced essentially parallel axes, means interconnecting said members for rotation about said axes in correspondence but reversely, and a signal take off unit pivotally connected to said two members at two eccentric points respectively which remain at equally spaced distances fiom a line joining said axes as the members turn, said unit comprising a potentiometer actuable in accordance With the movement of said points on the members to which said unit is connected and thereby actuable in accordance with a trigonometric function of the angular positioning of said points.

2. Apparatus as recited in claim 1, in which said means comprise teeth on said members interconnecting them for said rotation reversely, and said potentiometer comprises a linear potentiometer extensible and contractible in accordance with movements of said points relatively apart and together.

3. Apparatus as recited in claim 1, in which said potentiometer has a contact movably engaging a resistor element, and said resistor element has a center tap at an intermediate position of said contact.

4. Apparatus as recited in claim 3, in which said center tap is located at the position of said contact when said points are farthest from said line joining said axes.

5. Apparatus as recited in claim 1, in which said potentiometer is a linear motion linear winding potentiometer.

6. A trigonometric resolver comprising two members mounted for rotation about spaced essentially parallel axes, means interconnecting said members for rotation about said axes in correspondence but reversely, and a signal take off unit pivotally connected to said two members at two eccentric points respectively which remain at equally spaced distances from a line joining said axes as the members turn, said unit being actuable in accordance with the movement of said points on the members to which said unit is connected and thereby actuable in accordance with a trigonometric function of the angular positioning of said points.

7. Apparatus as recited in claim 6, in which said means comprise meshing gear teeth on said members interconnecting them for said rotation reversely.

8. Apparatus as recited in claim 6, in which said take ofi unit comprises an electrical unit controlling an output signal in accordance with said trigonometric function.

9. Apparatus as recited in claim 6, in which there is a second of said units connected to said members at eccentric points offset 90 about said axes from said first mentioned points whereby said units are actuable in accordance with the sine and cosine respectively of said angular positioning of the first mentioned points.

10. Apparatus as recited in claim 9, in which said two units are two linear motion linear winding potentiometers having center taps, and said means comprise gear teeth on said members interconnecting them for said rotation reversely.

11. Apparatus as recited in claim 6, including additional means for indicating which quadrant said members are in within their range of rotary movement.

12. Apparatus as recited in claim 11, in which said additional means comprise rotary contact means turning in accordance with said members, and stationary contact means engaged by said rotary contact means during only a predetermined portion of the rotary range thereof.

References Cited in the file of this patent UNITED STATES PATENTS 1,296,439 Sperry Mar. 4, 1919 FOREIGN PATENTS 1,049,448 France Aug. 19, 1953 736,085 Great Britain Aug. 31, 1955 

